Add files via upload

Author: suwarnarajput

Chapter 1/01_Thinking_Probabilistically_a_Bayesian_Inference_Primer (3).ipynb

@@ -0,0 +1,59 @@
+from __future__ import division
+import numpy as np
+import scipy.stats.kde as kde
+
+def hpd_grid(sample, alpha=0.05, roundto=2):
+    """Calculate highest posterior density (HPD) of array for given alpha. 
+    The HPD is the minimum width Bayesian credible interval (BCI). 
+    The function works for multimodal distributions, returning more than one mode
+
+    Parameters
+    ----------
+    
+    sample : Numpy array or python list
+        An array containing MCMC samples
+    alpha : float
+        Desired probability of type I error (defaults to 0.05)
+    roundto: integer
+        Number of digits after the decimal point for the results
+
+    Returns
+    ----------
+    hpd: array with the lower 
+          
+    """
+    sample = np.asarray(sample)
+    sample = sample[~np.isnan(sample)]
+    # get upper and lower bounds
+    l = np.min(sample)
+    u = np.max(sample)
+    density = kde.gaussian_kde(sample)
+    x = np.linspace(l, u, 2000)
+    y = density.evaluate(x)
+    #y = density.evaluate(x, l, u) waitting for PR to be accepted
+    xy_zipped = zip(x, y/np.sum(y))
+    xy = sorted(xy_zipped, key=lambda x: x[1], reverse=True)
+    xy_cum_sum = 0
+    hdv = []
+    for val in xy:
+        xy_cum_sum += val[1]
+        hdv.append(val[0])
+        if xy_cum_sum >= (1-alpha):
+            break
+    hdv.sort()
+    diff = (u-l)/20  # differences of 5%
+    hpd = []
+    hpd.append(round(min(hdv), roundto))
+    for i in range(1, len(hdv)):
+        if hdv[i]-hdv[i-1] >= diff:
+            hpd.append(round(hdv[i-1], roundto))
+            hpd.append(round(hdv[i], roundto))
+    hpd.append(round(max(hdv), roundto))
+    ite = iter(hpd)
+    hpd = list(zip(ite, ite))
+    modes = []
+    for value in hpd:
+         x_hpd = x[(x > value[0]) & (x < value[1])]
+         y_hpd = y[(x > value[0]) & (x < value[1])]
+         modes.append(round(x_hpd[np.argmax(y_hpd)], roundto))
+    return hpd, x, y, modes

Chapter 1/hpd (1).py

@@ -0,0 +1,98 @@
+from __future__ import division
+import numpy as np
+from scipy import stats
+import matplotlib.pyplot as plt
+from hpd import hpd_grid
+
+
+def plot_post(sample, alpha=0.05, show_mode=True, kde_plot=True, bins=50, 
+    ROPE=None, comp_val=None, roundto=2):
+    """Plot posterior and HPD
+
+    Parameters
+    ----------
+
+    sample : Numpy array or python list
+        An array containing MCMC samples
+    alpha : float
+        Desired probability of type I error (defaults to 0.05)
+    show_mode: Bool
+        If True the legend will show the mode(s) value(s), if false the mean(s)
+        will be displayed
+    kde_plot: Bool
+        If True the posterior will be displayed using a Kernel Density Estimation
+        otherwise an histogram will be used
+    bins: integer
+        Number of bins used for the histogram, only works when kde_plot is False
+    ROPE: list or numpy array
+        Lower and upper values of the Region Of Practical Equivalence
+    comp_val: float
+        Comparison value
+        
+
+    Returns
+    -------
+
+    post_summary : dictionary
+        Containing values with several summary statistics
+
+    """       
+
+    post_summary = {'mean':0,'median':0,'mode':0, 'alpha':0,'hpd_low':0,
+                   'hpd_high':0, 'comp_val':0, 'pc_gt_comp_val':0, 'ROPE_low':0,
+                   'ROPE_high':0, 'pc_in_ROPE':0}
+
+    post_summary['mean'] = round(np.mean(sample), roundto)
+    post_summary['median'] = round(np.median(sample), roundto)
+    post_summary['alpha'] = alpha
+
+    # Compute the hpd, KDE and mode for the posterior
+    hpd, x, y, modes = hpd_grid(sample, alpha, roundto)
+    post_summary['hpd'] = hpd
+    post_summary['mode'] = modes
+
+    ## Plot KDE.
+    if kde_plot:
+            plt.plot(x, y, color='k', lw=2)
+    ## Plot histogram.
+    else:
+        plt.hist(sample, normed=True, bins=bins, facecolor='b', 
+        edgecolor='w')
+
+    ## Display mode or mean:
+    if show_mode:
+        string = '{:g} ' * len(post_summary['mode'])
+        plt.plot(0, label='mode =' + string.format(*post_summary['mode']), alpha=0)
+    else:
+        plt.plot(0, label='mean = {:g}'.format(post_summary['mean']), alpha=0)
+
+    ## Display the hpd.
+    hpd_label = ''
+    for value in hpd:
+        plt.plot(value, [0, 0], linewidth=10, color='b')
+        hpd_label = hpd_label +  '{:g} {:g}\n'.format(round(value[0], roundto), round(value[1], roundto)) 
+    plt.plot(0, 0, linewidth=4, color='b', label='hpd {:g}%\n{}'.format((1-alpha)*100, hpd_label))
+    ## Display the ROPE.
+    if ROPE is not None:
+        pc_in_ROPE = round(np.sum((sample > ROPE[0]) & (sample < ROPE[1]))/len(sample)*100, roundto)
+        plt.plot(ROPE, [0, 0], linewidth=20, color='r', alpha=0.75)
+        plt.plot(0, 0, linewidth=4, color='r', label='{:g}% in ROPE'.format(pc_in_ROPE))
+        post_summary['ROPE_low'] = ROPE[0] 
+        post_summary['ROPE_high'] = ROPE[1] 
+        post_summary['pc_in_ROPE'] = pc_in_ROPE
+    ## Display the comparison value.
+    if comp_val is not None:
+        pc_gt_comp_val = round(100 * np.sum(sample > comp_val)/len(sample), roundto)
+        pc_lt_comp_val = round(100 - pc_gt_comp_val, roundto)
+        plt.axvline(comp_val, ymax=.75, color='g', linewidth=4, alpha=0.75,
+            label='{:g}% < {:g} < {:g}%'.format(pc_lt_comp_val, 
+                                                comp_val, pc_gt_comp_val))
+        post_summary['comp_val'] = comp_val
+        post_summary['pc_gt_comp_val'] = pc_gt_comp_val
+
+    plt.legend(loc=0, framealpha=1)
+    frame = plt.gca()
+    frame.axes.get_yaxis().set_ticks([])
+    return post_summary
+    
+

Chapter 1/mauna_loa_CO2 (1).csv

@@ -1,2 +1,55 @@
-# Bayesian-Analysis-with-Python
-Bayesian Analysis with Python by Packt
+#Bayesian Analysis with Python
+This is the code repository for [Bayesian Analysis with Python](https://www.packtpub.com/big-data-and-business-intelligence/bayesian-analysis-python?utm_source=github&utm_medium=repository&utm_campaign=9781785883804), published by Packt. It contains all the supporting project files necessary to work through the book from start to finish.
+##Instructions and Navigations
+All of the code is organized into folders. Each folder starts with a number followed by the application name. For example, Chapter02.
+
+
+
+The code will look like the following:
+```
+n_params = [1, 2, 4]
+p_params = [0.25, 0.5, 0.75]
+x = np.arange(0, max(n_params)+1)
+f, ax = plt.subplots(len(n_params), len(p_params), sharex=True, 
+  sharey=True)
+for i in range(3):
+    for j in range(3):
+        n = n_params[i]
+        p = p_params[j]
+        y = stats.binom(n=n, p=p).pmf(x)
+        ax[i,j].vlines(x, 0, y, colors='b', lw=5)
+        ax[i,j].set_ylim(0, 1)
+        ax[i,j].plot(0, 0, label="n = {:3.2f}\np = 
+         {:3.2f}".format(n, p), alpha=0)
+        ax[i,j].legend(fontsize=12)
+ax[2,1].set_xlabel('$\\theta$', fontsize=14)
+ax[1,0].set_ylabel('$p(y|\\theta)$', fontsize=14)
+ax[0,0].set_xticks(x)
+```
+
+This book is written for Python version >= 3.5, and it is recommended that you use 
+the most recent version of Python 3 that is currently available, although most of the 
+code examples may also run for older versions of Python, including Python 2.7 with 
+minor adjustments.
+Maybe the easiest way to install Python and Python libraries is using Anaconda, 
+a scienti fi c computing distribution. You can read more about Anaconda and 
+download it from https://www.continuum.io/downloads. Once Anaconda is in 
+our system, we can install new Python packages with this command: conda install 
+NamePackage.
+We will use the following python packages:
+•  Ipython 5.0
+•  NumPy 1.11.1
+•  SciPy 0.18.1
+•  Pandas  0.18.1
+•  Matplotlib 1.5.3
+•  Seaborn 0.7.1
+•  PyMC3 3.0
+
+##Related Products
+* [Expert Python Programming](https://www.packtpub.com/application-development/expert-python-programming?utm_source=github&utm_medium=repository&utm_campaign=9781847194947)
+
+* [Learning Bayesian Models with R](https://www.packtpub.com/big-data-and-business-intelligence/learning-bayesian-models-r?utm_source=github&utm_medium=repository&utm_campaign=9781783987603)
+
+* [Mastering Probabilistic Graphical Models Using Python](https://www.packtpub.com/big-data-and-business-intelligence/mastering-probabilistic-graphical-models-using-python?utm_source=github&utm_medium=repository&utm_campaign=9781784394684)
+###Suggestions and Feedback
+[Click here](https://docs.google.com/forms/d/e/1FAIpQLSe5qwunkGf6PUvzPirPDtuy1Du5Rlzew23UBp2S-P3wB-GcwQ/viewform) if you have any feedback or suggestions.